Improve scale height consistency

[The9Cat]

The Issue

exp and pyEXP make cylindrical bases assuming a $\mbox{sech}^2(z/h)$ vertical disk profile. This is not standard and scales as $\propto e^{-2z/h}$ at large values of $z$. As Jason points out: Agama uses $\mbox{sech}^2(z/2h)$ which scales as $\propto e^{-z/h}$ at large values of $z$.

This is confusing. It seems that this latter version is the standard in astronomy. In the short term, I propose adding a new exp and pyEXP parameter, sech2 which changes the disk conditioning function to use $\mbox{sech}^2(z/2h)$.

In the long run, we can deprecate the feature by adding oldsech2 to get the original behavior, followed by dropping the parameter altogether.

[The9Cat]

Another fall-back option is to create new C++ version of cylcache which exactly duplicates the Python version; specifically simply reads a YAML config and calls the basis factory.

[The9Cat]

I agree with both of your points:

1. We should not be maintaining the original cylcache and the equivalent pyEXP workflow (e.g. using the script or in a notebook). Since pyEXP seems to be the default, we should stick to that.
2. I'm in favor of allowing exp to be built without the Python3 build environment available. No Python3 implies no pybind11 and no pyEXP and no interpreter creation for user target density instances.

Notes

• The latest commit replaces the featureful utils/ICs/cylcache with a simple call to the BasisClasses::Basis::factory() constructor and adds CMake logic to turn on/off pybind11 code if Python3 is not detected. The old version has become bloated, so I think it's time to retire it.
• The new cylcache was tested using the default parameter set with MPI and OpenMP.
• I have not tested a compile without a Python3 environment; I don't have a straightforward way to do that. A hand-rolled Docker build could be coerced into that, I suppose.

[Copilot]

Pull Request Overview

Copilot reviewed 54 out of 55 changed files in this pull request and generated 5 comments.

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[Copilot]

Logic error: the conditions should check if the values are negative (not set), not positive. Should be 'if (I1min<0)' and 'if (I1max<0)' to match the initialization values and the comment context.

Suggested change

	if (I1min>0) I1min = Emin;
	if (I1max>0) I1max = Emax;
	if (I1min<0) I1min = Emin;
	if (I1max<0) I1max = Emax;

[michael-petersen]

Actually I'm realising this might be wrong, depending on how energy is defined (e.g. positive or negative). Can we fix and also add a comment here about the logic?

[The9Cat]

Oh, yeah, that's a mess. I'll comment a proposed fix.

[The9Cat]

Committed update.

[michael-petersen]

Actually I'm realising this might be wrong, depending on how energy is defined (e.g. positive or negative). Can we fix and also add a comment here about the logic?

(Referring to lines 579-580, and the commit below)

[Copilot]

Pull Request Overview

Copilot reviewed 54 out of 55 changed files in this pull request and generated 6 comments.

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[michael-petersen]

Lots of changes here; but standard workflows still operate as expected, and this does bring definitions in line with the literature.

No compile problems, will assume we are good to go now.